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Consistent changes in the sea ice seasonal cycle in response to global warming

Ian Eisenman ∗

California Institute of Technology, Pasadena, California, and University of Washington, Seattle, Washington

Tapio SchneiderCalifornia Institute of Technology, Pasadena, California

David S. Battisti and Cecilia M. BitzUniversity of Washington, Seattle, Washington

ABSTRACT

It has been widely noted that sea ice retreats faster in summer than winter in the Northern Hemi-sphere, both in observations and in projections from state-of-the-art climate models. Explanationsfor why the wintertime sea ice cover should be less sensitive to global warming have been proposed.However, in the Southern Hemisphere sea ice retreats fastest in winter in climate model projections.Here we show that the inter-hemispheric differences can be attributed to differences in coastlinegeometry. After accounting for this geometry, we find that the sea ice changes simulated in bothhemispheres in most climate models are consistent with sea ice retreat being fastest in winter inthe absence of landmasses. These results demonstrate that despite the widely differing rates ofice retreat among climate model projections, the seasonal structure of the sea ice retreat is robustamong the models and uniform in both hemispheres.

1. Introduction

The extent of sea ice covering the ocean in the highnorthern latitudes varies between about 7 Mm2 at summerminimum and 15 Mm2 at winter maximum in today’s cli-mate (with 1 Mm2 = 106 km2). During recent decades,Arctic sea ice has been rapidly retreating. The summerminimum of the ice extent has diminished considerablymore rapidly than the winter maximum (e.g., Serreze et al.2007), with an associated increase in the amplitude of theseasonal cycle (Figs. 1A, 2). These changes can also beviewed in the context of first-year and multi-year compo-nents of the sea ice cover, a common distinction based onwhether or not the ice has survived a summer melt season.In the approximation that all of the ice at summer mini-mum survives the winter growth season, the winter max-imum first-year ice extent is equivalent to the amplitudeof the ice extent seasonal cycle (Comiso 2002; Zhang andWalsh 2006). The increased seasonal cycle amplitude ofArctic sea ice extent, or similarly the increase in first-yearice extent, typically features prominently in assessments ofrecent observed changes in the Arctic sea ice (e.g., Nghiemet al. 2007; Kwok et al. 2009; Perovich et al. 2009).

The observed changes can be compared with globalwarming projections from state-of-the-art coupled atmosphere-ocean global climate models (GCMs) which were carried

out for the Coupled Model Intercomparison Project phase3 (CMIP3), the results of which were used for the In-tergovernmental Panel on Climate Change Fourth Assess-ment Report (Solomon et al. 2007). GCM projections varywidely in terms of the rate of Arctic sea ice loss (Fig. 3),making it difficult to obtain a reliable estimate for thetimescale of future ice retreat (cf. DeWeaver 2007; Boeet al. 2009; Wang and Overland 2009). However, the Arc-tic sea ice extent seasonal cycle is consistently amplified asthe climate warms in most of the GCMs (Fig. 2A,B), whichhas been identified as one of the most striking features ofthe Northern Hemisphere sea ice projections (Zhang andWalsh 2006). Hence the GCM projections suggest thatwhatever is causing Arctic sea ice retreat to be fastest insummer may be expected to continue in the future.

In contrast to the Northern Hemisphere, observationsreveal very little long-term change in Southern Hemisphereice extent, with the trend being toward a slight increase(Fig. 2D,E). Although the positive trend in Southern Hemi-sphere annual-mean sea ice extent is statistically significant(e.g., Comiso and Nishio 2008), the seasonal differences inthe rate are small, and there is no significant change inthe seasonal cycle amplitude (see Appendix A). Hence theobserved sea ice cover in the Southern Hemisphere has notchanged sufficiently to carry implications regarding howthe ice extent seasonal cycle amplitude responds to climate

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change.GCM projections, however, show Southern Hemisphere

sea ice retreat that is fastest in winter (Fig. 2D,E), oppo-site to what occurs in the Northern Hemisphere (Fig. 1A).Although this feature can be readily seen in previously pub-lished results (Arzel et al. 2006; Solomon et al. 2007, Fig.10.13), scant discussion of it exists in the literature.

Most previously published physical mechanisms for changesin the sea ice extent seasonal cycle have focused on ob-served changes in the Arctic. A standard explanation sug-gests that thin ice reforms in winter wherever air is suffi-ciently cold but quickly melts during the following summer,causing the summer ice extent to be more sensitive thanthe winter ice extent to thermodynamic changes induced byincreased greenhouse gases (e.g., Meier et al. 2005). Sum-mer minimum ice extent anomalies have also been pro-posed to be amplified by seasonally-dependent factors in-cluding the ice-albedo feedback (Lindsay and Zhang 2005;Perovich et al. 2007), downward longwave radiative fluxanomalies (Francis and Hunter 2007), and changes in oceanheat transport driven by the penetration of wind forcingthrough the sea ice cover (Shimada et al. 2006). However,explanations for the ice retreat being fastest at summerminimum that rely on basic thermodynamic processes andfeedbacks are inconsistent with the simulated ice retreatbeing fastest in winter in the Southern Hemisphere.

Alternatively, natural variability in atmospheric circu-lation has been proposed as an explanation for a substantialfraction of the observed loss of summer Arctic sea ice ex-tent, with wind-driven ice advection during winter leadingto thinner ice that is more easily melted during the follow-ing summer (Rigor et al. 2002). This mechanism was sup-ported by observed correlations during the early and mid-1990s, and an associated longer-term reduction in the ageof the ice cover was suggested to explain the continued iceretreat thereafter despite the sign of the correlations revers-ing (Rigor and Wallace 2004). More recently, correlationswith another index of atmospheric circulation have beensuggested to explain a significant fraction of the observedtrend in summer minimum sea ice extent (Ogi et al. 2010).Explanations for the ice retreat being fastest at summerminimum that rely on natural variability in wind forcing,however, are at odds with the Northern Hemisphere seaice extent seasonal cycle amplitude increasing during theentire 21st century in GCM simulations.

Changes in the sea ice extent seasonal cycle in bothhemispheres are summarized schematically in Fig. 1A. Dueto the vast differences in the rate of retreat (Fig. 3), wechoose a coordinate system here that does not dependon rate. In Fig. 2C,F, the ice extent seasonal cycle am-plitude in each hemisphere is plotted versus the annual-mean ice extent. As the annual-mean sea ice edge mi-grates poleward, the observed and simulated sea ice extentseasonal cycle increases in the Northern Hemisphere (Fig.

2C), whereas the simulated sea ice extent seasonal cycle de-creases in the Southern Hemisphere (Fig. 2F). This studyexamines why the response of the sea ice extent seasonalcycle to global warming is opposite between the two hemi-spheres.

2. Effect of landmass distribution

Among the wide array of differences in climate betweenthe two hemispheres, we isolate the effect of landmass dis-tribution as the factor likely to have the most pronouncedeffect on the sea ice cover. In the Northern Hemisphere,there is little land poleward of 75◦N, but extensive landsouth of this rims the Arctic Ocean (Fig. 4A). As a result,the sea ice edge is obstructed by land throughout the yearexcept near the time of summer minimum ice extent. In theSouthern Hemisphere, by contrast, the Antarctic continentextends from the pole to about 70◦S, but there is little landequatorward of this in the latitudes spanning the SouthernOcean (Fig. 4C). Hence the Southern Hemisphere sea iceedge rarely touches land.

We focus here on the simple obstruction of sea ice bylandmasses. The shape of the Northern Hemisphere coast-line causes changes in the sea ice edge latitude to havea muted effect on sea ice extent during much of the year(Fig. 4A). In Eisenman (2010), it was proposed that sea-sonal asymmetries in Arctic sea ice evolution ranging fromthe shape of the seasonal cycle to the unprecedented lossin September 2007 can be explained in terms of this mut-ing. Here we follow that work’s definition of “equivalentextent” as the total land plus ocean surface area polewardof the zonal-mean sea ice edge. The equivalent extent canbe approximately visualized by drawing a straight line be-tween the sea ice edge on either side of each landmass andfilling in the region poleward of this line with sea ice. Thisprovides a rough approximation of what the sea ice extentmight be if all the land were removed.

The equivalent extent is proportional to the sine of thezonal-mean ice edge latitude (Eisenman 2010). In this workwe focus on the equivalent extent, rather than on the iceedge latitude, to facilitate comparison with sea ice extent inthe Southern Hemisphere, where the sea ice edge evolves ina nearly land-free geography. If the Northern Hemispherezonal-mean ice edge latitude migrates poleward at a ratethat is constant year-round, as is the case during recentdecades in observations (Eisenman 2010), the ice extentdecreases most rapidly in summer (larger white area be-tween solid and dashed red lines than between blue linesin Fig. 4A). Wintertime changes in the ice edge have aconsiderably larger effect on equivalent extent than on ex-tent, however, and in this scenario the equivalent extentdecreases most rapidly in winter (larger white plus grayarea between blue lines than between red lines in Fig. 4A).

We compute the sea ice equivalent extent from the sea

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ice extent using a two-step process. First, the latitude char-acterizing the sea ice edge is approximated by finding thelatitude which has an ocean area poleward of it equal to theice extent (arrows pointing right in Fig. 4B,D). Next, theequivalent extent is computed as the total land plus oceanarea poleward of this latitude (arrows pointing left in Fig.4B,D). This process is carried out for the ice extent timeseries from observations and GCMs in both hemispheres,with the transfer function being computed separately fromthe land masks in each GCM (see Appendix B) and in theobserved fields (see Appendix A).

3. Results

The observed and simulated changes in sea ice equiva-lent extent in both hemispheres are plotted in Fig. 5. In theNorthern Hemisphere, the summer minimum equivalent ex-tent (Fig. 5A) is similar to the summer minimum extent(Fig. 2A). However, because the wintertime sea ice edgeresides at a latitude with a large land fraction, the win-ter maximum equivalent extent (Fig. 5B) is considerablylarger and retreats faster than the winter maximum extent(Fig. 2B). As expected from the cartoon in Fig. 4A, thisinfluence of land is sufficient to cause the seasonal structureof the Northern Hemisphere ice retreat to be reversed: incontrast to the extent, the equivalent extent seasonal cy-cle amplitude decreases as the ice edge moves poleward inboth observations and GCMs (Fig. 5C).

In the Southern Hemisphere, the equivalent extent (Fig.5D-E) evolves similarly to the extent (Fig. 2D-E) with theaddition of a constant equal to the area of the Antarcticcontinent. Changes in the summer minimum equivalentextent (Fig. 5D) are somewhat enhanced compared withextent changes (Fig. 2D) due to the ice edge touching theAntarctic coastline (Fig. 4C), but the summer minimumequivalent extent still retreats more slowly than the wintermaximum equivalent extent. Hence, after accounting forthe muting effect of landmasses on sea ice extent changes,the seasonal cycle in equivalent extent decreases in bothhemispheres as the ice edge migrates poleward (Fig. 5C,F,Fig. 1B).

The decreasing equivalent extent seasonal cycle ampli-tude in response to global warming occurs not only in theensemble mean in both hemispheres (Fig. 5C,F), but also inmost individual GCMs. In Fig. 6, the change during 1900–2100 in the equivalent extent seasonal cycle amplitude ineach of the 21 GCMs is plotted. The wide spread in hori-zontal coordinates for either hemisphere is an indication ofthe inter-model differences in the simulated rate of retreat.The bunching of points near a diagonal line indicates thatalthough the models do not agree on the amount of ice re-treat, they do largely agree that the more the annual-meanice cover diminishes (farther to left in Fig. 6), the smallerthe equivalent extent seasonal cycle becomes (farther down

in Fig. 6). The agreement among the models on this pointis in stark contrast with their projections for the timelineof sea ice changes (Fig. 3). The central message of Fig. 6 isthat the sea ice equivalent extent seasonal cycle diminishesin response to global warming in both hemispheres in mostmodels (i.e., most points lie in the lower quadrant of theplot).

4. Discussion

These results allow a comparison between GCM sim-ulations and observations. As has been noted previously(Stroeve et al. 2007), the observed retreat in summer min-imum ice extent (red curve in Fig. 3A) is faster than theretreat in most GCM simulations (thin curves in Fig. 3A).Furthermore, annual-mean sea ice extent, which can be vi-sually approximated by the average between summer min-ima and winter maxima in Fig. 2, diminishes by approxi-mately the same amount in both hemispheres during 1900–2100 in the GCM simulations, in contrast to observed changesduring recent decades. The simulated Northern Hemi-sphere ice extent diminishes slowly during the 20th cen-tury and then more rapidly during the 21st century (Fig.2A,B), whereas the simulated Southern Hemisphere ice ex-tent diminishes at a more constant rate during 1900-2100(Fig. 2D,E). These differences between GCMs and obser-vations emerge similarly when viewed from the perspectiveof equivalent extent: the slopes of the red and blue curvesduring 1979–2009 in Fig. 5A differ by 60%. For the North-ern Hemisphere annual-mean equivalent extent versus time(not shown), the slopes differ similarly by 50%. When plot-ted in a coordinate system that does not depend on the rateof retreat, however, GCMs and observations in the North-ern Hemisphere show better agreement, with the slopes ofthe red and blue curves in Fig. 5C during 1979–2009 (usingyearly data) differing by only 3%. Note that the red andblue curves are displaced from each other in Fig. 5C dur-ing this time period by 10% in both horizontal and verticaldirections.

Discussions comparing sea ice in the two hemispherestypically find more differences than similarities (e.g. Dieck-mann and Hellmer 2010). For example, sea ice in theNorthern Hemisphere grows primarily through congelationat the ice–ocean interface, whereas in the Southern Hemi-sphere, where snow accumulation rates are larger, muchof the growth occurs at the surface due to flooding underthe weight of snow (Petrich and Eicken 2010). In Fig. 2,the Southern Hemisphere sea ice extent seasonal cycle isconsiderably larger than that in the Northern Hemisphere,with summer and winter extremes both being outside theNorthern Hemisphere seasonal range. After accounting forland, however, the sea ice cover seasonal cycles in the twohemispheres become more similar (Fig. 5). The wintermaximum equivalent extent is nearly identical in the two

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hemispheres in simulations of the 20th century, but the iceedge is farther poleward at summer minimum in the North-ern Hemisphere. In Fig. 5C (Northern Hemisphere), theslope of the seasonal cycle amplitude versus annual-meanequivalent extent evolution is 0.5, and in Fig. 5F (SouthernHemisphere) the slope is relatively similar at 0.4. Similarly,in Fig. 6, the distributions for both hemispheres are neareach other and both seem to fall near the same diagonalline.

In addition to illuminating the similarities between thesea ice evolutions in the two hemispheres, the equivalentextent may be a useful metric for comparing models be-cause it addresses differences in model coastlines. Totalsea ice cover in GCM simulations is typically compared interms of ice extent (e.g., Zhang and Walsh 2006). Thereare considerable inter-model differences, however, in theland masks associated with the sea ice concentrations (i.e.,fractional sea ice cover) in the CMIP3 archive. Grid boxeswith land fractions between 0 and 1 are treated as land insome models but as ocean in others, and ice shelves aretreated as land glaciers in some models but as sea ice inothers. This causes the ocean area poleward of 70◦, forexample, to vary by more than 1 Mm2 among the models,with the inter-model standard deviation being 0.9 Mm2

in the Northern Hemisphere and 0.4 Mm2 in the South-ern Hemisphere. In other words, two GCMs may simulateNorthern Hemisphere sea ice extents that differ by 1 Mm2

when both are identically simulating a sea ice cover thatextends to 70◦N. These effects of land mask differences arenaturally addressed when instead using sea ice equivalentextent.

In this analysis, we have followed the standard conven-tion of defining ice extent as the area of grid boxes withsea ice concentration of at least 15%. For a given sea icecover, this definition depends on grid resolution. The seaice concentration grids for the GCM data in the CMIP3archive typically have resolutions on the order of 50–100km, whereas the observed sea ice extent is calculated us-ing a nominally 25 km grid. Sea ice area, defined as thesum of grid box areas scaled by the ice concentration ineach box, is independent of resolution, but it is more proneto systematic errors in satellite-derived observations (e.g.,Parkinson and Cavalieri 2008). Using sea ice area insteadof extent, and hence calculating a sea ice equivalent area,does not qualitatively influence the results presented here(not shown).

Some GCMs become seasonally ice free during the 1900–2100 simulation period. This edge effect could in principlelead to winter sea ice cover retreating faster than summerice cover after the latter reaches 0 (cf. Fig. 1). In Fig. 7A,the results of Fig. 6 are repeated for each hemisphere ex-cluding all models that simulate less than 0.1 Mm2 sea iceextent in that hemisphere at any point during 1900-2100.Comparison of the two figures demonstrates that this effect

does not qualitatively affect the results presented in Fig. 6.The physical mechanism causing sea ice equivalent ex-

tent to decrease more rapidly in winter than summer isexpected to differ from previously proposed mechanisms,since the latter were aimed at explaining why NorthernHemisphere ice retreat is fastest in summer. Several hintsregarding the cause of the changes in the sea ice seasonalcycle can be gleaned from the GCM simulations. First, allbut one of the GCMs include horizontal ice motion andrheology. The model INM CM3.0 (#12 in Fig. 6), how-ever, simulates the sea ice as motionless. That this liesnear the middle of the distribution in both hemispheres isevidence that horizontal ice motion is not a primary fac-tor. Second, there is considerably more simulated snow-fall on the sea ice in the Southern Hemisphere than in theNorthern Hemisphere (Solomon et al. 2007, Fig. 8.5), whichis typically associated with the difference in land fractionimmediately equatorward of the sea ice cover. Addition-ally, ocean circulation is considerably different between thetwo hemispheres. That the equivalent extent seasonal cy-cle changes similarly in both hemispheres is evidence thatsnow cover and ocean circulation are not dominant factors.Third, five CMIP3 GCMs reported sea ice changes in equi-librium simulations of CO2 doubling that did not include adynamic ocean (see Appendix B). The results of these sim-ulations are plotted in Fig. 7B. Similar to Fig. 6, most of thepoints lie in the lower quadrant, which demonstrates thatthe equivalent extent seasonal cycle amplitude decreases inresponse to global warming in both hemispheres in most ofthese GCMs even in the absence of changes in ocean heatflux convergence. Taken together, these results implicatethe interaction between sea ice and atmospheric processesas a likely source of the changes in the sea ice seasonalcycle.

In summary, Northern Hemisphere sea ice extent di-minishes faster in summer than winter in observations andGCM projections. Southern Hemisphere sea ice extent,by contrast, diminishes fastest in winter. The results pre-sented here show that after accounting for landmasses thatrim the Arctic Ocean, the changes in the sea ice coverin both hemispheres are consistent with ice retreat beingfastest in winter in the absence of land. This diminishedsea ice cover seasonal cycle in response to warming is ro-bust among the range of GCMs and uniform in both hemi-spheres.

Acknowledgments.

IE was supported by a Prize Postdoctoral Fellowshipthrough the Caltech Division of Geological and PlanetarySciences and a NOAA Climate and Global Change Post-doctoral Fellowship administered by the University Corpo-ration for Atmospheric Research. We thank the modelinggroups and the Program for Climate Model Diagnosis andIntercomparison for making available the CMIP3 multi-

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Fig. 1. Schematic illustrating the difference between the rate of change at summer minimum and winter maximum inboth hemispheres. (A) Sea ice extent (as plotted in Fig. 2). (B) Sea ice equivalent extent (as plotted in Fig. 5), whichrepresents a rough approximation of what the ice extent would be in the absence of landmasses. Thin double-headedarrows on the right in panel A identify the amplitude of the seasonal cycle. Thick arrows below the curves indicate therate of change at summer minimum and winter maximum. Curves are drawn from satellite-derived daily sea ice extent(Cavalieri et al. 1996), with equivalent extent computed as described in the text. The lengths of the thick arrows areexaggerated to highlight the points discussed here.

model dataset.

APPENDIX A

Satellite-derived Observations

Data processing

Monthly-mean ice extent observations in both hemi-spheres are derived from passive microwave satellite mea-surements during Jan 1979–Dec 2009 (Fetterer et al. 2002).Months with missing values (in both hemispheres, Dec1987 and Jan 1988) are filled with linear interpolation be-tween the same month in the previous year and followingyear. We use the NSIDC land mask associated with sea iceconcentrations from Nimbus-7 SMMR and DMSP SSM/Isatellite measurements to compute sea ice equivalent ex-tent.

Statistical significance in Southern Hemisphere

The annual-mean sea ice extent in the Southern Hemi-sphere increases during 1979-2009 with a linear trend of0.15 Mm2/decade, or 1.2%/decade when scaled by the 1979-2000 mean. This trend is significant above the 99.7% con-fidence interval (i.e., white noise would produce a trendthis far from zero less than 0.3% of the time). The trendin the ice extent seasonal cycle amplitude as a function oftime, however, is not distinguishable from zero at even the

68% confidence interval. The same applies for the trend inthe yearly ice extent seasonal cycle amplitude versus yearlyannual-mean ice extent, as well as the trend in the 5–yearaverages of these quantities (red points in Fig. 2F).

APPENDIX B

Climate Models

Coupled Atmosphere–Ocean Simulations

We include in this analysis 21 of the 24 coupled atmosphere–ocean GCMs that participated in CMIP3, excluding two(GISS EH and NCAR PCM) that have not reported seaice concentration fields to the CMIP3 archive for the sim-ulations we analyze and one (LASG FGOALS-g1.0) thathas a known bias toward vast overestimation of sea ice ex-tent and is typically excluded from sea ice analyses (e.g.,Zhang and Walsh 2006). For each model, ice extent during1900-2100 is calculated as the total area of grid boxes withat least 15% sea ice concentration in the “Climate of the20th Century” simulation, and ice extent during 2000-2100is calculated in the same way from the “SRES A1B” sim-ulation. When multiple ensemble members are available,we consider only the first member.

Land masks for computing equivalent extent in eachGCM were obtained using one of several techniques. Formany of the GCMs, land grid boxes were reported as miss-ing values in the sea ice concentration field. For GCMs

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Fig. 2. Observed and simulated changes in sea ice extent in both hemispheres. The Northern Hemisphere (A) summerminimum and (B) winter maximum ice extent are plotted based on monthly-mean satellite-derived observations (seeAppendix A) and simulations from 21 coupled atmosphere–ocean GCMs (see Appendix B). (C) The seasonal cycleamplitude is plotted as a function of the annual-mean ice extent, with 20–year averages taken of the ensemble mean and5–year averages taken for the observations, which span only 31 years. (D)-(F) Same as (A)-(C) but for the SouthernHemisphere. The simulated change in the Southern Hemisphere ice extent seasonal cycle amplitude (panel F) is oppositeto the Northern Hemisphere (panel C). Observed Southern Hemisphere changes show very little structure in this context(panel F). Vertical scales in panels A, B, D, and E are all identical.

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Fig. 3. Differences among the GCM projections of the rate of Arctic sea ice loss. (A) Timeline toward seasonally ice-freeArctic Ocean conditions indicated by September Northern Hemisphere sea ice extent during the 21st century scaled bythe 1980–2000 mean September value for each model. (B) Sea ice retreat during the entire 21st century (September extentat 2080–2100 scaled by September extent at 1980–2000) in each GCM. In the ensemble mean, 32% of the September seaice cover remains at the end of the century, but projections vary widely among the GCMs from a model that retains morethan 85% of the ice to 4 models retaining less than 1%.

that instead reported land grid boxes as having zero seaconcentration, either missing values in the sea surface tem-perature field reported by the ocean component or nonzerovalues in the land area fraction reported by the atmospherecomponent (which always had values of either 0 or 1 forthese models) were used, depending on whether the sea icecomponent in each GCM shared its grid with the ocean orthe atmosphere.

Atmosphere–Ocean Simulations

We also consider atmosphere–only simulations above aslab ocean with specified ocean heat flux convergence (i.e.,“ocean q-flux”). Sea ice concentration for these simulationswas reported to the CMIP3 archive by 5 of the 24 GCMs.To assess the change in the sea ice cover in response toCO2 doubling, we calculate the sea ice extent time seriesfrom the “slab ocean control” simulation and the “2xCO2equilibrium” simulation, and then we compute the meanice extent seasonal cycle during the final 20 years of eachsimulation. Note that HadGEM1 becomes seasonally icefree in both hemispheres in the “2xCO2 equilibrium” sim-ulation but none of the other 4 GCMs simulate less than0.1 Mm2 ice extent in either hemisphere.

Land masks in the slab ocean simulations are identicalto the coupled simulations from the same GCM with theexception of HadGEM1, in which the sea ice concentrationwas reported on the atmosphere grid in the former but on

the ocean grid in the latter.

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Fig. 4. Cartoon of landmass distributions in both hemispheres and schematic illustrating the calculation of sea iceequivalent extent from extent. (A) Cartoon of Northern Hemisphere geography, with gray indicating land and whiteindicating ocean. The latitude of the sea ice edge associated with summer minimum (red) and winter maximum (blue)ice cover at the beginning (solid) and end (dash) of the simulated period is included based on the ensemble mean iceedge latitude during 1900–1920 and 2080–2100. The total white area enclosed within a given ice edge line indicates theice extent, and the total white plus gray area enclosed within the line indicates the equivalent extent. (B) Mappingfunction used to calculate the sea ice equivalent extent from the extent. The blue line indicates the mapping of a typicalNorthern Hemisphere winter maximum ice extent to equivalent extent. Beginning with the ice extent (lower intersectof blue line with vertical axis), the latitude with area poleward of it equal to the extent is computed (intersect betweenblue and orange lines). Next, the total land plus ocean area poleward of this latitude is identified as the equivalentextent (upper intersect of blue and orange lines). The red line indicates the mapping for a typical summer minimum iceextent, illustrating that the difference between equivalent extent and extent is considerably larger at winter maximumthan at summer minimum. (C)-(D) Same as (A)-(B) but for Southern Hemisphere. Here the difference between extentand equivalent extent is similar at winter maximum (blue line) and at summer minimum (red line).

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m2

1900 2000 2100

24

30

36

C

Ann Mean EqExt (Mm2)

δE

qExt

(Max

–Min

,M

m2)

14 18 22

21

23

25Ensemble Mean, 20yr avgsObservations, 5yr avgs

Time (yr)

D

South

ern

Hem

ispher

e

Sum

mer

Min

EqE

xt(M

m2)

4.2

Mm

2

1900 2000 2100

6

12

18

24

Time (yr)

E

Win

ter

Max

EqE

xt(M

m2)

6.1

Mm

2

1900 2000 2100

30

36

42

F

Ann Mean EqExt (Mm2)

δE

qExt

(Max

–Min

,M

m2)

22 24 26

20

21

Fig. 5. Observed and simulated changes in sea ice equivalent extent in both hemispheres. Panels are as in Fig. 2. Incontrast to the extent, the equivalent extent seasonal cycle responds to global warming similarly in both hemispheres(panels C,F). Note that observed equivalent extent changes in the Southern Hemisphere cluster near the point (26, 18)in panel F and are not included in the plotted vertical range.

9

1

1

2

2

3

3

4

4

55

6

6

7

7

8

8

9

9 10

10

11

11

12

12

13

13

14

14

15

1516

16

17

1718

18

19

19

20

20

21

21

Change in Ann Mean EqExt (Mm2)

Chan

gein

!E

qExt

(Mm

2) NH

SH

−20 −10 0−20

−10

0

10 Simulated 1900-21001. BCCR BCM2.0 (Norway)2. CCCMA CGCM3.1 T47 (Canada)3. CCCMA CGCM3.1 T63 (Canada)4. CNRM CM3 (France)5. CSIRO MK3.0 (Austral ia)6. CSIRO MK3.5 (Austral ia)7. GFDL CM2.0 (USA)8. GFDL CM2.1 (USA)9. GISS AOM (USA)10. GISS ER (USA)11. INGV SXG (Italy)12. INM CM3.0 (Russia)13. IPSL CM4 (France)14. MIROC3.2 medres (Japan)15. MIROC3.2 hi res (Japan)16. MIUB ECHO-G (Germany/Korea)17. MPI ECHAM5 (Germany)18. MRI CGCM2.3.2 (Japan)19. NCAR CCSM3.0 (USA)20. UKMO HadCM3 (UK)21. UKMO HadGEM1 (UK)

• Observed 1979-2009 !4

Fig. 6. Robustness among models. The change in the equivalent extent seasonal cycle amplitude during 1900–2100in each GCM is plotted versus the change in annual-mean equivalent extent for the Northern Hemisphere (red) andthe Southern Hemisphere (blue). Vertical and horizontal coordinates here are equivalent to the vertical and horizontaldisplacements in Fig. 5C,F evaluated separately for each model. That all points lie to the left of the origin indicatesthat all GCMs simulate a loss of annual-mean ice cover in both hemispheres in response to increased greenhouse gases.More striking is the feature that most points lie below the origin, indicating that most GCMs simulate a reduction in thesea ice equivalent extent seasonal cycle in both hemispheres. Observed Northern Hemisphere changes during the shorter31–year period are included in the figure after being scaled by a factor of 4. Changes during 1900–2100 are computed bymultiplying by 2 the difference between the temporal mean during the first and last 100 years; changes during 1979–2009are computed similarly using the first and last 15 years.

1

1

2

2

3

3

55

6

6

7

9

10

1011

12

12

13

16

16

17

18

18

19

20

20

21

21

Change in Ann Mean EqExt (Mm2)

Chan

gein

δE

qExt

(Mm

2) A

−20 −10 0−20

−10

0

10

22 3355

18

18

21

21

Change in Ann Mean EqExt (Mm2)

Chan

gein

δE

qExt

(Mm

2) B

−20 −10 0−20

−10

0

10

Fig. 7. Influence of edge effects and ocean dynamics on robustness among models. (A) As in Fig. 6, except that for eachhemisphere, models with ice extent less than 0.1 Mm2 at any time during 1900–2100 are excluded. (B) As in Fig. 6, butconsidering atmosphere–only equilibrium climate sensitivity simulations rather than coupled atmosphere–ocean transientsimulations (see Appendix B). Here the differences between the climate under doubled CO2 and the control simulationare plotted.

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